Project #1863 - Statistics 1

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In all three parts of this question, you are a statistical consultant in a research lab.

Part 1

A medical research worker prepares and reports cholesterol data for two groups of six patients each. The researcher submits the following to you, the statistician, and asks whether the treatment significantly altered the cholesterol readings in either direction(use p = 0.05 as the cutoff for statistical significance).

Control

Treated

362

194

211

277

320

201

276

164

288

304

321

199

You call the researcher after receiving the data.There were only the data – no write-up of how the experiment was done.(FYI: This is called a protocol.)The researcher has left for a two-week vacation in Florida, but the assistant assures you that the control patients were a different set than the treated patients and the two groups (total of 20) were randomly selected.You are to perform the appropriate two-sample test on the data (α-level 0.05) and write a report for the researcher.

e.Report to the researcher (2 POINTS): Write brief statements on the results of both the confidence interval and the hypothesis test.

Part 2

It is two weeks later.Back from Florida, the researcher reads your report and finds that you did not treat the data as paired!They were, in fact, paired – the patients were tested first, then given the medication and tested again!The assistant had misinformed you!(Hey, this happens !!!).The correct table is

Patient 1

Patient 2

Patient 3

Patient 4

Patient 5

Patient 6

Pre-treatment

362

211

320

276

288

321

Treated

194

277

201

164

304

199

You must now redo the report.Use alpha-level 0.05 as before.

a.Summary statistics (1 POINTS):

Difference

Mean

Standard Deviation

b.Test (1 POINTS):

HO

HA

c.p – value is (1 POINTS) _______

d.95% Confidence Interval around the mean (1 POINTS):(,)

e.Report to the researcher (2 POINTS): Write statements on the results of both the confidence interval and the hypothesis test.

f.Add to your report a short tactful, clear, grammatically correct explanation of why it was necessary to redo the statistical analysis.In your report, tell what the difference was in your conclusion and explain the difference between independent and paired samples in a way that a non-statistician would understand.Remember: Be tactful! (2 POINTS)

Part 3

A week has passed.The researcher e-mails you and is writing his report.His boss asks him for a specific recommendation on whether the medication should be mass-produced (yes or no!)The researcher is apprehensive about making the wrong decision.For the correct hypothesis that you tested,

a.Describe to the researcher in terms of his study what the Type I error is.What could be the effect on the company? (2 POINTS)

b.Describe to the researcher in terms of his study what the Type II error is.What could be the effect on the company? (2 POINTS)

c.By now, you are very unsure about the researcher.You begin to wonder if the

assumptions and conditions have been met for the correct t-test that you did.

Name the assumptions and conditions for the test and describing them in a way